The magnetic susceptibility of biomaterials generates a local magnetic field and provides a very important contrast mechanism in MRI, such as T2*-weighted imaging, susceptibility-weighted imaging (SWI) (see Haacke E M, Xu Y, Cheng Y C, Reichenbach J R. (2004) Susceptibility weighted imaging (SWI). Magn Reson Med 52(3):612-618 (“Haccke (2004)”) and quantitative susceptibility mapping (QSM) (see de Rochefort L, Nguyen T, Brown R, Spincemaille P, Choi G, Weinsaft J, Prince M R, Wang Y. (2008) In vivo quantification of contrast agent concentration using the induced magnetic field for time-resolved arterial input function measurement with MRI. Medical physics 35(12):5328-5339 (“de Rochefort (2008a)”); de Rochefort L, Liu T, Kressler B, Liu J, Spincemaille P, Wu J, Wang Y. (2009) A Weighted Gradient Regularization Solution to the Inverse Problem from Magnetic Field to Susceptibility Maps (Magnetic Source MRI): Validation and Application to Iron Quantification in the Human Brain. Proc ISMRM 462; de Rochefort L, Brown R, Prince M R, Wang Y. (2008b) Quantitative MR susceptibility mapping using piece-wise constant regularized inversion of the magnetic field. Magn Reson Med; 60(4):1003-1009 (“de Rochefort (2008b)”); Liu T, Spincemaille P, de Rochefort L, Kressler B, Wang Y. (2009) Calculation of susceptibility through multiple orientation sampling (COSMOS): a method for conditioning the inverse problem from measured magnetic field map to susceptibility source image in MRI. Magn Reson Med 61(1):196-204 (“Liu (2009)”); Kressler B, de Rochefort L, Liu T, Spincemaille P, Jiang Q, Wang Y. (2009) Nonlinear Regularization for Per Voxel Estimation of Magnetic Susceptibility Distributions From MRI Field Maps. IEEE transactions on medical imaging (“Kressler (2009)”); Li L, Leigh J S. (2004) Quantifying arbitrary magnetic susceptibility distributions with MR. Magnet Reson Med 51(5):1077-1082 (“Li (2004)”); Shmueli K, de Zwart J A, van Gelderen P, Li T Q, Dodd S J, Duyn J H. (2009) Magnetic susceptibility mapping of brain tissue in vivo using MRI phase data. Magn. Reson. Med. 62(6): 1510-1522 (“Shmueli (2009)”)).
It has been reported that accurate QSM can be generated by combining information from magnitude and phase images (de Rochefort L, Liu T, Kressler B, Liu J, Spincemaille P, Lebon V, Wu J, Wang Y. (2010) Quantitative susceptibility map reconstruction from MR phase data using bayesian regularization: validation and application to brain imaging. Magn. Reson. Med. 63(1): 194-206 (“de Rochefort (2010)”). For appropriate phase masking in SWI and accurate susceptibility quantification in QSM (Fernandez-Seara M A, Techawiboonwong A, Detre J A, Wehrli F W. (2006) MR susceptometry for measuring global brain oxygen extraction. Magn Reson Med 55(5):967-973 (“Fernandez-Seara (2006)”), it is necessary to separate the local field in a given region of interest (ROI) from the background field. This background field arises from various sources, including imperfect shimming and magnetic susceptibility sources outside the ROI (both inside and outside the imaging volume). For example, in brain imaging, the air-tissue interfaces near the skull and various air cavities induce a strong background field variation extending deep into the brain. The background field is superimposed onto the local fields generated by venous blood, iron deposition and calcifications, impeding clear visualization of the local details in SWI and introducing errors in QSM.
Current background removal techniques assume that the local and background fields in a space spanned by the Fourier basis (see Wang Y, Yu Y, Li D, Bae K T, Brown J J, Lin W, Haacke E M. (2000) Artery and vein separation using susceptibility-dependent phase in contrast-enhanced MRA. J Magn Reson Imaging 12(5):661-670 (“Wang (2000)”)) or polynomial functions are separable (see de Rochefort (2008b); Langham M C, Magland J F, Floyd T F, Wehrli F W. (2009) Retrospective correction for induced magnetic field inhomogeneity in measurements of large-vessel hemoglobin oxygen saturation by MR susceptometry. Magn Reson Med 61(3):626-633 (“Langham (2009)”); Yao B, Li T Q, Gelderen P, Shmueli K, de Zwart J A, Duyn J H. (2009) Susceptibility contrast in high field MRI of human brain as a function of tissue iron content. Neuroimage 44(4):1259-1266 (“Yao (2009)”)), or require a priori knowledge of the spatial distribution of all background susceptibility sources (see Neelavalli J, Cheng Y C, Jiang J, Haacke E M. (2009) Removing background phase variations in susceptibility-weighted imaging using a fast, forward-field calculation. J Magn Reson Imaging 29(4):937-948 (“Neelavalli (2009)”); Koch K M, Papademetris X, Rothman D L, de Graaf R A. (2006) Rapid calculations of susceptibility-induced magnetostatic field perturbations for in vivo magnetic resonance. Physics in medicine and biology 51(24):6381-6402 (“Koch (2006)”)). The assumption of the separability between local and background fields in a certain space is often violated, leading to erroneous estimation of local fields, and the results depend on the choice of the basis functions (see Langham (2009)). In practice, the knowledge of the background susceptibility source surrounding a given ROI is often not fully available or sufficiently accurate, particularly when there are significant variations in susceptibility outside the imaging field of view (FOV), leading to a substantial residual background field that requires additional attention (see Neelavalli (2009)). A reliable background field removal method is the use of reference scans, in which an identical object but with the susceptibility sources removed is scanned to measure the reference background field (see de Rochefort (2008b); Liu (2009)). However, it is impractical or impossible to perform a reference scan in many in vivo situations.